We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization-group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process $(M\ensuremath{-}H$ curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization, susceptibility, and specific heat of the zigzag chain in magnetic fields at finite temperatures, and then discuss how the calculated quantities reflect the low-lying excitations of the system related with the critical behaviors in the $M\ensuremath{-}H$ curve.
Thermodynamic properties of a tetrameric bond-alternating Heisenberg spin chain with ferromagnetic-ferromagnetic-antiferromagnetic-antiferromagnetic exchange interactions are studied using the transfer-matrix renormalization group and compared to experimental measurements. The temperature dependence of the uniform susceptibility exhibits typical ferrimagnetic features. Both the uniform and staggered magnetic susceptibilities diverge in the limit $T\ensuremath{\rightarrow}0$, indicating that the ground state has both ferromagnetic and antiferromagnetic long-range orders. A double-peak structure appears in the temperature dependence of the specific heat. Our numerical calculation gives a good account for the temperature and field dependence of the susceptibility, the magnetization, and the specific heat for $\mathrm{Cu}{(3\text{\ensuremath{-}}\mathrm{Clpy})}_{2}{({\mathrm{N}}_{3})}_{2}$ $(3\text{\ensuremath{-}}\mathrm{Clpy}=3\text{\ensuremath{-}}\text{Chloroyridine})$.
Thermodynamic properties of the quantum Heisenberg spin chains with
S=1/2, 1, and
3/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
The magnetic and thermodynamic properties of spin-
1∕2 Heisenberg diamond chains are investigated in three different cases: (a)
J1,
J2,
J3>0 (frustrated), (b)
J1,
J3<0,
J2>0 (frustrated), and (c)
J1,
J2>0,
J3<0 (nonfrustrated), where the bond coupling
Ji (i=1,2,3)>0 stands for an antiferromagnetic (AF) interaction, and
<0 for a ferromagnetic (F) interaction. The density-matrix renormalization-group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer-matrix renormalization-group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin-correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor
S(q) shows peaks at wave vectors $q=a\ensuremath{\pi}∕3$
(a=0,1,2,3,4,5) for different couplings in a zero magnetic field, which, however, in the magnetic fields where the magnetization plateau with
m=1∕6 pertains, exhibits the peaks only at
q=0, $2\ensuremath{\pi}∕3$, and $4\ensuremath{\pi}∕3$, which are found to be couplings independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the magnetization, susceptibility, and specific heat show various behaviors for different couplings. The double-peak structures of the susceptibility, and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the
XXZ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat, and magnetization for the compound
Cu3(CO3)2(OH)2 are fairly compared with our TMRG results.
The magnetization process, the susceptibility, and the specific heat of the spin-
1∕2 antiferromagnet (AF)-AF-ferromagnet (F) and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at
m=1∕6 for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.
We study the magnetic properties of two types of one-dimensional
XX spin-
21 chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.